If The Beam Will Fail In The Static, Initial Loading Case

The ultimate objective of this problem will be to determine whether it is safe for this beam to operate. First the static (load applied once) case should be assessed, while the repeated loading case is given as a bonus question.

The drawing below depicts a machined AISI 1020 steel beam with a rectangular cross-section that is undergoing a cyclic load. The load, F, varies from 250 N to 500 N under each cycle. The material’s ultimate tensile strength, Sut, is 470 MPA. The beam is rigidly supported at the wall. Points A and B are just to the right of the wall. A is at the bottom of the beam. B is at the center of the beam. C is immediately adjacent to the notch and at half of the length. The notch is a half-circle extrusion and its diameter is 2 mm.

L = 500mm; w = 20mm; h = 40mm; for a square cross section, I = w*h^3/12; and transverse shear a square cross section, tau_max = 3/2*V/A

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8.1 Draw a free body diagram of the beam, exclude the wall, label axes (4 pts) – upload in file

8.2 Indicate the stresses acting on stress elements at points A and B (assume they are in the center of the beam with respect to width although this should not affect your results). Draw x-y plane stress elements. (8 pts) – upload in file

8.3 Calculate the Von Mises stress at points A, and B then report the higher value. (8 pts) – calculated in this question